Table of Contents
- 1 How do you prove that an equivalence relation is R?
- 2 Which of the following is true if the relation R on the set of integers is defined as?
- 3 How do you show an equivalence relation?
- 4 How do you show that a relationship is symmetric?
- 5 Is the relation R on the set R of real numbers?
- 6 How do you show a reflexive relationship?
How do you prove that an equivalence relation is R?
To prove R is an equivalence relation, we must prove R is reflexive, symmetric, and transitive. So let a, b, c ∈ R. Then a − a = 0=0 · 2π where 0 ∈ Z. Thus (a, a) ∈ R and R is reflexive.
Which of the following is true if the relation R on the set of integers is defined as?
A relation R is defined on the set of integers as xRy if f(x + y) is even.
Is the relation R in the set defined as reflexive?
In mathematics, a homogeneous binary relation R on a set X is reflexive if it relates every element of X to itself. An example of a reflexive relation is the relation “is equal to” on the set of real numbers, since every real number is equal to itself.
How do you show an equivalence relation?
To prove an equivalence relation, you must show reflexivity, symmetry, and transitivity, so using our example above, we can say:
- Reflexivity: Since a – a = 0 and 0 is an integer, this shows that (a, a) is in the relation; thus, proving R is reflexive.
- Symmetry: If a – b is an integer, then b – a is also an integer.
How do you show that a relationship is symmetric?
Symmetric Relation In other words, a relation R in a set A is said to be in a symmetric relationship only if every value of a,b ∈ A, (a, b) ∈ R then it should be (b, a) ∈ R. Here let us check if this relation is symmetric or not. We have seen above that for symmetry relation if (a, b) ∈ R then (b, a) must ∈ R.
How do you show that something is a equivalence relation?
Is the relation R on the set R of real numbers?
Show that the relation R in the set R of real numbers, defined as R = {(a, b): a ≤ b2} is neither reflexive nor symmetric nor transitive. ∴R is not reflexive. But, 4 is not less than 12. ∴R is not symmetric.
How do you show a reflexive relationship?
What is reflexive, symmetric, transitive relation?
- Reflexive. Relation is reflexive. If (a, a) ∈ R for every a ∈ A.
- Symmetric. Relation is symmetric, If (a, b) ∈ R, then (b, a) ∈ R.
- Transitive. Relation is transitive, If (a, b) ∈ R & (b, c) ∈ R, then (a, c) ∈ R. If relation is reflexive, symmetric and transitive,
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